Q: A medication decays in the bloodstream according to $$A(t) = 50(0.8)^t$$, where $$A is $$the amount in mg and $$t is $$time in hours. How much remains after 3 hours?

$$A(3) = 50 \times (0.8)^3$ = 25.6 mg$$

Q: A car's value depreciates by 15% each year. If the car is worth $20,000 now, what will it be worth in 3 years?

$$20,000 \times (0.85)^3$ = 12,282.5$$

Q: Which of the following best describes the end behavior of the polynomial $$f(x) = -2x^4$ + 5x^2$ - 3$$?

As $$x \to \pm\infty$$, $$f(x) \to -\infty$$

Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{2x - 8}$$?

Accepted Answer

$$x \geq 4$$

Question 2

A population of bacteria triples every 4 hours. If the initial population is 200, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 200 	imes 3$$^{t/4}$$

Question 3

Solve for $$x$$: $$2^{x+1} = 32$

Accepted Answer

$$x = 4$$

Question 4

Which of the following is the inverse function of $$f(x) = 5x - 7$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x+7}{5}$$

Question 5

A chemical reaction follows the equation $$C = 10e$$^{-0.2t}$$, where C$ is the concentration in mg/L and t$ is time in hours. What is the concentration after 5 hours?

Accepted Answer

$$C = 10e$$^{-1}$$ \approx 3.68 mg/L$$

Question 6

Which of the following is the correct factorization of the quadratic $$x^2 - 5x + 6$?

Accepted Answer

$$(x-2)(x-3)$$

Question 7

Given $$f(x) = x^2$ and g(x) = x+1$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$9$$

Question 8

A medication decays in the bloodstream according to $$A(t) = 50(0.8)^t$$, where $$A is $$the amount in mg and $$t is $$time in hours. How much remains after 3 hours?

Accepted Answer

$$A(3) = 50 	imes (0.8)^3$ = 25.6 mg$$

Question 9

Which of the following describes the transformation of the graph of $$y = x^2$ to y$$ = $$(x-3)^2 + 2$?

Accepted Answer

Shift right 3 units and up 2 units

Question 10

Solve the equation $$\log_2$(x) = 5$$ for $$x.$$

Accepted Answer

$$x = 32$$

Question 11

A rational function is given by $$f(x) = \dfrac{2x+1}{x-4}. $$What is the vertical asymptote?

Accepted Answer

$$x = 4$$

Question 12

If $$f(x) = 3x^2$ - 2x + 1$$, what is $$f(-2)$$?

Accepted Answer

$$17$$

Question 13

Which of the following is equivalent to $$\log_{10}(1000)$$?

Accepted Answer

$$3$$

Question 14

A rectangle has a length that is 3 times its width. If the perimeter is 48 units, what is the area?

Accepted Answer

$$216$$ square units

Question 15

Which of the following is the solution set for the inequality $$2x - 5 \u003c 7$$?

Accepted Answer

$$x \u003c 6$$

Question 16

If $$f(x) = x^3$ and g(x) = 2x$, what is f(g(2$$))$$?

Accepted Answer

$$64$$

Question 17

A car's value depreciates by 15% each year. If the car is worth $20,000 now, what will it be worth in 3 years?

Accepted Answer

$$20,000 	imes (0.85)^3$ = 12,282.5$$

Question 18

Which of the following is the range of the function $$f(x) = \dfrac{1}{x}$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 19

Solve for $$x$$: $$x^2 - 9x + 14 = 0$

Accepted Answer

$$x = 7 or$$ $$x = 2$$

Question 20

Which of the following best describes the end behavior of the polynomial $$f(x) = -2x^4$ + 5x^2$ - 3$$?

Accepted Answer

As $$x 	o \pm\infty$$, $$f(x) 	o -\infty$$

College Algebra Syllabus and Course Structure Study Guide

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드